Case study: designing a reduction with a 62.5 mm center distance
A step-by-step example to size a 1:1.5 reduction with a fixed center distance, choosing the correct module and integer tooth counts.
The machine frame imposes the center distance: exactly 62.5 mm, no exceptions. The required reduction ratio is 1:1.5, that is, the gear wheel must turn at 2/3 of the pinion's speed. Your task is to find the combination of module m, pinion tooth count Z1 and gear-wheel tooth count Z2 that satisfies both constraints, choosing among the standard modules and obtaining integer tooth counts.
Finding the product m × Z1
Start from the center-distance formula:
Knowing that Z2 = i × Z1, with i = 1.5, you can rewrite the equation and derive the product m × Z1:
This number, 50, must be the product of the module and the pinion tooth count. The whole sizing starts from here.
Trying the standard modules
Now break down 50 into the catalog modules, looking for the combinations that produce integer tooth counts for both the pinion and the gear wheel.
| Module m | Z1 = 50/m | Z2 = Z1 × 1.5 | Outcome |
|---|---|---|---|
| 1.0 | 50 | 75 | OK, but small teeth |
| 2.0 | 25 | 37.5 | Z2 not integer: discarded |
| 2.5 | 20 | 30 | OK: robust solution |
| 3.0 | 16.67 | — | Z1 not integer: discarded |
The solution
The winning combination is module 2.5, Z1 = 20 teeth, Z2 = 30 teeth.
Compared with module 1.0, also geometrically valid, module 2.5 guarantees more robust teeth, greater torque capacity and greater tolerance to center-distance errors. This counts especially when the frame is made from laser-cut sheet metal: tolerances can exceed two tenths of a millimeter, and a larger module absorbs these deviations better.
When you have several geometrically valid solutions, generally choose the largest module compatible with the footprint. You pay a few grams of extra weight and gain robustness, durability and assembly tolerance.
Final check: undercut control
Before closing the sizing, verify that Z1 is greater than 17. Below this threshold, milling the tooth can cut into the foot of the profile, weakening it: this is the undercut phenomenon, which in certain cases requires profile corrections to recover strength. In our case Z1 = 20, well above the limit, so no corrections are needed.
If your project should take you below this threshold, you don't need to change the module or center distance: there are profile-correction techniques that eliminate undercut while keeping the transmission geometry unchanged.
The 17-tooth threshold applies to the standard profile at 20° pressure angle. With different pressure angles or corrected wheels, the limit changes. If you work outside the standard profile, check the minimum tooth count in the catalog or in the sector ISO references.